Abstract：Uncertainty management is playing an important role in many fields，especially in AI (artificial intelligence). This paper introduces the concept of probability and the Bayesian Network which are widely used in uncertainty management field.Additionally， two examples are completed and analyzed in the paper.

Keywords：Uncertainty management;Probability;Bayesian network

1 INTRODUCTION(WHAT IS UNCERTAINTY?)

People always deal with all sorts of information everyday.However，most of the information for human is imperfect.This information is fuzzy，inconsistent or uncertain.When designing a system，what people can do is to make it as an ideal one.

However，the real world is often not ideal.When people want to cover whole situations，they may use imprecise data to describe the real situation. That means there is uncertainty in the system.It is not good idea to just ignore all the uncertain information.The better way to deal with it is to know how to do uncertainty management.

2 TYPE OF UNCERTAINTY

Uncertainty issues are partitioned into those that deal with fuzziness and those that deal with ambiguity.There are many types of uncertainty.And in Artificial Intelligence，uncertainty management is an important work to do.Basically，several types of uncertainty situation are as follows:

A.Inconsistency.This often arises when confliction occurs.This means there are two conditions，however， satisfying one of them means not satisfying another one.

B.Multiple options.People many have many tourism sites for them to choose.And it not clear which sites they may choose.The economic factor might decide which of them may be chosen.

C.Nondeterminism.When software is designed， people do not know whether the output will meet the requirement before testing it.In other words，it is not determined.

D.No knowledge as negation.In knowledge based system，if the one rule is not inside the system，then the opposite one is defaulted as true.For instance， if say“he was born in Shanghai.”when users ask system“is he from China?”，the system will say no. because programmer did not design the rule that he is from China. And obviously，this is not the fact.

E.Intepretation uncertainty.The weather forecast always states that“there is a 80% chance of raining tomorrow”.What does this mean?

3 PROBABILISTIC

Probabilistic is the earliest attempt to deal with uncertainty management.Particularly， Bayesian Network had been widely used in Artificial Intelligence to deal with uncertainty management. .

4 BAYESIAN NETWORK

A.Intruduction of bayesian network.Bayesian network was firstly introduced by Pearl in 1986， and has been an important part in AI.This network applies probability theory to handle the uncertainty in knowledge processing，and can transfer human expertise to a form which is conveniently for machine learning.

B.Structure of bayesian network.Normally， there are two main parts in Bayesian network，the first one is a diagram.The second one is the CPT (conditional probabilities table).

C.The reason for using Bayesian network.Theoretically，what people need in probability reasoning is joint probability.However，the complexity of joint probability will have the exponential increase of the number of variables.So it is very hard to do this when there are many variables.

And what the Bayesian network can do is to split the complex joint probability problem into several simple modules. And when people meet complex problem， it is possible to apply probability reasoning to solve it.

Additionally，the key concept of Bayesian network is conditional independence.

5 EXAMPLE FOR BAYESIAN NETWORK

A.Software available for Bayesian networks

Microsoft’s MSBNX

BNT

GeNIe

In the example below，GeNIe will be used for the medical diagnosis.

B.Introduction of the GeNIe.GeNIe is a development environment for building graphical decision-theoretic models.It has been developed at the decision system Laboratory，University of Pittsburgh.GeNIe’s name and its uncommon capitalization originate from the name Graphical Network Interface，given to the original simple interface to SMILE.

C.Introduction of the problem1.This is a Bayesian network problem.

There are several variables available for the problem，it is required to construct a Bayesian network incorporating the variables accurately according to the perception of the real world and discover the conditional independence properties of the network.

Working parents:both，father，mother，none

Household income:0-60000，60000-100000，more than 100000

Number of children:none，one，two， three，four and up

Religion:Christianity，Judaism，Islam，Buddhism， Atheism，other

Fish eating habits:often fish，rarely fish

Drinking habits: never alcohol， wine once in a while，often wine，wine everyday

Fiber eating habits:lots of fiber，not much fiber

History of illness:case of severe illness，often minor illness，rarely minor illness

Illness at the moment:severe illness，minor illness，no illness.

Fiber eating habits:lots of fiber，not much fiber.

D.Problem1 solving.In Bayesian network，the independence of each condition is very important. In this case，first thing to do is to find out which condition is related with another one，and discover the independent conditions accordingly.

We can assume the final outcome is the illness at the moment.So，this is actually a medical diagnosis decision making networks.

Based on several conditions，probability of the illness at the moment can be solved out by Bayesian network.

Explanation of the independence between several conditions is:

History of illness，fiber eating habits，drinking habits and fish eating habits are independent.

Number of children，history of illness，fiber eating habits，drinking habits are independent.

However，there are some conditions which are interrelated.

⑴Working habits is depended on religion.

⑵household income is depended on the working parents.

⑶fish eating habits are depended on the household income and number of children and religion.

⑷drinking habits is depended on the religion

⑸illness at the moment is depended on the history of illness，fiber eating habits，fish eating habits and drinking habits.

After deciding the inter-relationship between the conditions and the final outcome variable， the expertise of probability can be inputted into the Bayesian network.

For example， we assume the religion is Judaism， the number of children is four and up，the history of illness is rarely minor illness，then the outcomes will be as follows.

E.Introduction to problem2.A player is confronted with three doors A，B and C.Behind exactly one of the doors there is $10000.The money is yours if you choose the correct door.After you have made your first choice of door but still not opened it，and official comes in.He works according to some rules.

⑴He starts by opening a door.He will not open the door you have chosen，and he will not open the door which money is behind.

⑵After he opened a door，there will be two closed doors.He will ask you if you want to change your choice，you can stick to your first choice or you can choose the last door.

So the question is which one is a better choice? Stick to your first choice and switch it?

F.Problem2 solving.We can build the Bayesian network first，do the experiment and then analyze the procedure.

⑴For the first choice， the probability is obvious.The player has equal chance to open each of the three doors.

⑵For the prize behind the door，the situation is basically the same as the first choice， when the designer want to put the prize behind the door， he have three options，and he have equal chance for each option

⑶For the official’s choice，the probability is depending on the prize and the player’s first choice.

⑷First of all，the first choice can be chosen， for instance， the first choice is the first door.

Next，the official choice can be the third one.

Then the outcomes will be as follows:

So the probability of the prize in the first door is 1/3.

And the probability of the prize in the second door is 2/3.

This means the play will have a double probability for winning the prize if switching the choice.

6 CONCLUTION

In this paper，one way of dealing with Uncertainty Management is introduced.However，there are many other ways.

Fuzzy logic is essentially one way to deal with uncertainty，because Fuzziness of reality is one kind of uncertainty too..

[References]

[1]Perar l J.Fusion，propagation， and st ructuring in belief network.Ar tificial Intelligence[M].Vol.29，No.3，1986，241-288.

[2]Michael Negnevitsky，Artifical Intelligence，1st ed，[M]. AddisonWesley，Boston:15-26.

[3]Stuart Russel，Peter Norvig，Artificial Intelligence，A Modern Approach[M].3rd Edition，(Prentice Hall):56-78.

[4]G.J.Klir and B.Yuan，F(xiàn)uzzy Sets and Fuzzy Logic[M].(Prentice Hall PTR， 1995):122-143.

[5]R.E.Walpole and R.H.Myers，Probability and Statistics for Engineers and Scientists[M].4th ed.(Macmillan，1989):1-10.

[6]Bayes' theorem，Wikipedia.http://en.wikipedia.org/wiki/Bayes%27_theorem.